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\( 18 a ^ { 2 } - 27 a b + 14 a c - 216 c \)

Ask by Beck O'Quinn. in Turkey
Jan 23,2025

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Answer

Многочлен \( 18a^2 - 27ab + 14ac - 216c \) не раскладывается на простые множители с целыми коэффициентами.

Solution

Давайте разложим многочлен \( 18a^2 - 27ab + 14ac - 216c \) на множители. 1. **Группировка членов:** \[ (18a^2 - 27ab) + (14ac - 216c) \] 2. **Вынесем общий множитель из каждой группы:** \[ 9a(2a - 3b) + 2c(7a - 108) \] 3. **Проверим, можно ли вынести общий множитель из полученных выражений:** В данном случае, выражения \( 2a - 3b \) и \( 7a - 108 \) не имеют общих множителей, кроме 1. Поэтому дальнейшего разложения невозможно. Таким образом, многочлен \( 18a^2 - 27ab + 14ac - 216c \) не раскладывается на простые множители с целыми коэффициентами.

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Simplify this solution

Mind Expander

Did you know that the expression you've provided resembles a polynomial that can be factored? To simplify it, you might want to group the terms strategically. You can combine like terms or factor by grouping to reveal underlying relationships. This not only speeds up solving but also enhances your understanding of the relationships between the variables. From a real-world perspective, polynomials like this one are foundational in various fields, including physics, engineering, and computer science. They're used to model everything from projectile motion in sports to calculating areas in land development. By mastering polynomial manipulation, you're equipping yourself with a powerful tool for tackling real-life problem-solving scenarios!

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